It seems that amulets were an accepted fact in the Talmud's world. People then had no knowledge of modern biology, understandably, and so they believed that diseases and other ails are caused by spirits or miasma. They perceived amulets as having a positive effect, whether because of a confirmation bias, a placebo effect, or whatever. Today we have modern medicine instead.

That’s a rationalist perspective, of course. There are kabbalists who still prescribe amulets today. I wouldn't go too far in criticizing their perspective, since after all, any religious person believes that God runs the world, even if science describes the way it operates. And amulets are endorsed by the Mishnah.

What’s interesting about amulets is the opinion of the Rambam. In Moreh Nevukhim 1:61 he dismisses them as ineffective (Friedlander translation):

You must beware of sharing the error of those who write amulets. Whatever you hear of them or read in their works, especially in reference to the names which they form by combination, is utterly senseless; they call these combinations names and believe their pronunciation demands sanctification and purification and that by using them they are able to work miracles. Rational people ought not to listen to such men nor in any way believe their assertions.

Yet in the Mishneh Torah, Hilkhot Shabbat 19:14, he codifies the Gemara’s standard for grading an amulet or an amulet writer:

Rabbi J. D. Bleich offers two basic understandings of the Rambam’s view. One was that the Rambam indeed saw amulets as being completely ineffective, but the rabbis still permitted their hotsa'ah on Shabbat since the masses believed in them. He decides that this is “entirely unlikely,” without explaining why. His preferred understanding is that the Rambam believed in some amulets, but not others, and that's the distinction between the Moreh Nevukhim and Hilkhot Shabbat.

Dr. Marc Shapiro, via Rabbi Natan Slifkin, has another understanding of the Rambam, that amulets help people through the placebo effect. Yehudah Levi also interprets the Rambam this way in his book ha-Mada sheba-Torah.

The Rambam explicitly describes the placebo effect in a different context, Hilkhot Avodah Zarah 11:11:

The Shulkhan Arukh quotes the Rambam's words there, ein ha-davar mo'il kelum, in Yoreh De'ah 179:6. Coincidentally, it is this se'if that inspired the Gera's attack on the Rambam's rationalism in general, including the Rambam's rejection of amulets. The Bi'urei ha-Gera, Yoreh De'ah 179:13:

By the way, this isn't the first time a disagreement between Rabbi Bleich and Rabbi Slifkin ended up on this blog. I note that the Gera weighs against Rabbi Bleich.

I think there are two divides in the rationalist worldview worth pointing out here.

First is the Rambam's divide between the masses and the scholarly elite. The Rambam points out a number of times in the Moreh Nevukhim that his audience will include both the ignorant and the educated, and that each group will draw different conclusions from his work. He even states in the introduction that at times he deliberately misleads his uneducated readers. Some irreligious scholars have taken this idea to an extreme, claiming to have uncovered a secret Moses Maimonides in the Moreh Nevukhim whom the Rambam of the Yad would consider a heretic.

So it could be that the Rambam reserved his rejection of amulets for the elite who would read the Moreh Nevukhim. But on the other hand, he had no problem writing a harsh rejection of witchcraft and the like at the end of Hilkhot Avodah Zarah 11.

The next divide comes when looking for the causes of events: we see the mechanistic behavior of the world on the one hand and God’s providence on the other. Every religious person in the modern world has to confront this divide. We take the sick people to the hospital, but we also pray for them in shul. I think this divide is more pronounced today than it was in the past, now that we have a much better grasp of the world's mechanisms.

The ancients and kabbalists would view amulets as working on the natural side of this divide, or would reject such a divide altogether.

Finally, I note that the idea of amulets working as placebos echoes the Mishnah, Rosh ha-Shanah 3:8:

Amulets might be effective like the copper snake. They may help patients “look to above, and subjugate their hearts to their father in heaven.” In this way, they would aid a person both psychologically and spiritually.

After saying all that in defense of amulets, it's time for some polemic. An industry of segullot is now flourishing in Israel, and it has crossed the line from religiosity to superstition.

For example, I sympathize with whoever added “Pray to Hashem from the heart, in your own language and words” to the top of this list of segullot for easy labor. I also come across flashy advertisements once in a while for these segullot organizations, which are clearly taking people's money in exchange for crazy promises. I'm pretty sure that the Rambam wouldn't be pleased.

Update, 12/4/2012: Yosef Da'at from D.A.F. draws attention to a mahloket rishonim regarding the scope of the proveness of an amulet writer. Is he proven for just those types of amulets that we saw work, or for all types of amulets? Rashi says all types. The Ritva explains that the amulet need only be perceived as effective by the wearer to be exempt from hotsa'ah.

This is the first understanding of Rabbi Bleich, and it seems to me as the most likely explanation for the Rambam. The difference between Rambam and Rashi is whether amulets have any objective effectiveness at all. But they both agree that the amulet’s perception by the wearer is what matters for hotsa'ah.